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Abstract

We suggest a new type of grating reflector denoted hybrid grating (HG) which shows large reflectivity in a broad wavelength range and has a structure suitable for realizing a vertical cavity laser with ultra-small modal volume. The properties of the grating reflector are investigated numerically and explained. The HG consists of an un-patterned III–V layer and a Si grating. The III–V layer has a thickness comparable to the grating layer, introduces more guided mode resonances and significantly increases the bandwidth of the reflector compared to the well-known high-index-contrast grating (HCG). By using an active III–V layer, a laser can be realized where the gain region is integrated into the mirror itself.

Figures (7)

(a) and (b) show schematic cross-sectional views of an HCG and an HG, respectively. In both cases a plane wave is incident from the top in the surface normal direction and similar results can be obtained for incident light from bottom. ni and ti represent refractive index and thickness of each part, respectively. Λ and f denote the periodicity and duty cycle of the grating. (c) and (d) are dispersions of leaky modes (blue curves) and reflectivity spectra (green curves) for the HCG and the HG, respectively. k0 = 2π/λ0, and β is the real part of propagation constant of a leaky mode. The red curves show the appeared resonance due to individual GMRs which will overlap to make the total reflectivity spectra (green curves)

Contour plot of transmissivity in dB as a function of wavelength, grating thickness, tg, and cap layer thickness, tc. In the upper graph, tg is increased from 0.497 μm to 1.997 μm while tc is zero. In the lower graph, tc is increased from 0 to 1.5 μm while tg is kept to 0.497 μm. The white dashed line shows the cap layer thickness of the HG structure considered in Fig. 2 and the circles indicate the wavelengths of the four GMRs.

SFGs of the propagating modes in each layer for (a) HCG and (b) HG structure. Black dots represent propagating modes at each layer. Red arrows denote the interactions between the modes which take place at interfaces. Circular arrows mean self coupling (reflectivity of a mode to itself) at interfaces.

(a) Schematic cross-sectional view of the HG with considered modes in each layer. (b) The equivalent reflectivity from the two interface of the cap layer and grating. (c) Calculated reflectivity spectrum of the structure shown in Fig. 2 using full RCWA (red solid line) and with discarding non-propagating modes (blue dashed line). It shows a very good agreement especially in the wavelength region with high reflectivity.